Semi-analytic expressions for quasinormal modes of slowly rotating Kerr black holes

Abstract

We provide semi-analytic expressions for quasinormal mode frequencies of slowly rotating Kerr black holes to the quadratic order in the rotation parameter. We apply the parametrized black hole quasinormal mode ringdown formalism to the Chandrasekhar-Detweiler equation and the Sasaki-Nakamura equation instead of the Teukolsky equation, and compare our result with the previous numerical calculations.

An alternative to the Teukolsky equation

“…In Table I, we show the first twelve perturbative coefficients to the fundamental QNM frequency for (s, ) = (−2, 2) obtained in this way. The first and second order corrections are perfectly consistent with a recent computation in a different approach [26]. Now we compare these results with numerical data.…”